Question

The displacement x (in centimetres) of an oscillating particle varies with time t (in seconds) as
$x=2cos(0.5\pi t+\frac{\pi }{3})$
The magnitude of the maximum acceleration of the particle in $cm{s}^{-2}$ is

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{4}$
• C. $\frac{{\pi }^2}{2}$
• D. $\frac{{\pi }^2}{4}$

Answer 1

The correct option is C

$\frac{{\pi }^2}{2}$

Given that, $x=2cos(0.5\pi t+\frac{\pi }{3})$
$\therefore$ Velocity, $v=\frac{dx}{dt}=-2\times 0.5\pi sin(0.5\pi t+\frac{\pi }{3})$
and acceleration, $a=\frac{dv}{dt}=-2\times 0.5\pi \times 0.5\pi cos(0.5\pi t+\frac{\pi }{3})$
$\therefore$ Maximum acceleration, $a_{max}=-2\times 0.5\pi \times 0.5\pi =-\frac{{\pi }^2}{2}cm{s}^{-2}$
and the magnitude of maximum acceleration, $|a_{max}|=|-\frac{{\pi }^2}{2}|=\frac{{\pi }^2}{2}cm{s}^{-2}$
Hence, the correct choice is (c).